hi OP 
what a situation to be in. My heart goes out to you- my (now ex)H did something similar just over a year ago, and I ended up in the abyss a few months later. You love your H, and it hurts but he really is, and has been a complete bastard and you need to be able to get on with your life.
^ I completely second a previous poster who says you need proper child access arrangements. He cannot keep coming into the house every day- you need your own space for yourself and the children, and to get your own routines. If he wants to see the children, he needs to have them wherever he is staying. Any change of routine though (going somewhere else) needs to be on a gradual basis for the children's wellbeing. It sounds like your H is trying to have his cake and eat it- he wants to be part of the family when it is convenient to him, and he is in control of the situation. It needs to stop. FWIW my ex did the whole coming round 4 times plus per week when we first separated (I had him back stupid me- I loved him) and I can completely relate to how you feel. It absolutely tears you apart. And he will take advantage of that.
Have you talked to your RL friends about what has happened between your H and yourself? As sometimes having a whole host of people who are pointing out the fact that has has been a complete and utter arsehole is helpful. It is so easy when you are in constant contact to have the wool pulled over your eyes as it is hard to reconcile that part of them that has betrayed you- whilst you were pregnant!! with the man that you love.
Have you seen a solicitor at all? Can you afford to? I found filing for divorce to be very therapeutic- having in writing what a complete git my H had been was momentous.
Seriously though- this is a hard time. You need help and support. It is going to be hard, but it gets easier. One year down the line and things are getting better, but I wouldn't have been able to do it without my friends and the MH services. I was surprised at how much my friends were happy to help e.g. we all went out for dinner on my wedding anniversary, when I said I'd like to do something as I would find that date hard. I doubt your friends will tell you to buck up- they will know people who have been in similar situations. They will know that the whole situation will be immensely stressful.
I wish I'd asked for help from the MH services sooner- go and see your GP and tell them how you feel. Be honest. It is vital that you ask for help- your children need you. You may think that the world will be better off without you- unless you are a terrorist/evil dictator that is completely untrue. For your children you ARE their world and they would much rather have a mum who is sad and struggling for a while than no mum at all. Things will be difficult for some time but you don't have to feel suicidal, you can have support to find a way through, it is out there. And things will get easier with time.
This time last year I was devastated, a complete mess and thinking similar thoughts to you. Now I can confidently say I would never, under any circumstances, want to get back with my lying, cheating ex! You can do it, but you do need some help